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A222314 Number of characters when n-th row of Pascal's triangle is written in base 10 (including the n spaces). 2
1, 3, 5, 7, 9, 13, 16, 19, 22, 27, 35, 39, 43, 51, 58, 65, 73, 81, 87, 95, 108, 117, 124, 137, 149, 159, 168, 181, 194, 207, 221, 233, 247, 263, 278, 291, 304, 325, 341, 355, 374, 397, 414, 431, 455, 473, 493, 517, 538, 555, 579, 605, 625, 643, 672, 697, 716, 743, 769, 795, 820, 847, 870, 899, 929, 957, 981, 1011, 1046, 1077, 1107, 1139, 1173 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Inspired by Fig. 1 of Cobeli and Zaharescu.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..2000

C. Cobeli and A. Zaharescu, Promenade around Pascal Triangle-Number Motives, Bull. Math. Soc. Sci. Math. Roumanie, Tome 56(104) No. 1, 2013, 73-98.

N. J. A. Sloane, Triangle showing silhouette of first 30 rows of Pascal's triangle (after Cobeli and Zaharescu)

FORMULA

Stirling's formula shows that a(n) ~ n^2/(2 log 10) = 0.217... n^2.

EXAMPLE

"1 6 15 20 15 6 1" contains 16 characters, so a(6) = 16.

MAPLE

lis:=[];

M:=100;

f1:=n->[seq(binomial(n, k), k=0..n)];

for n from 0 to M do

t1:=f1(n);

t2:=convert(t1, string);

t3:=length(t2)-2-n;

lis:=[op(lis), t3];

od:

[seq(lis[i], i=1..M)];

PROG

(PARI) a(n) = n + sum(k=0, n, #digits(binomial(n, k))); \\ Michel Marcus, Aug 29 2015

CROSSREFS

Cf. A007318.

Sequence in context: A243910 A211136 A178653 * A228232 A182058 A200975

Adjacent sequences:  A222311 A222312 A222313 * A222315 A222316 A222317

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Feb 16 2013

STATUS

approved

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Last modified February 26 03:09 EST 2020. Contains 332272 sequences. (Running on oeis4.)